A calculus problem by أحمد الحلاق

Calculus Level 4

\[ \large \lim_{x\to0} \dfrac{5^{3x} - 5^x - 5^{2x} + 1}{\sqrt{1+\cos x} - \sqrt2} \]

The limit above has a closed form. Find the value of this closed form.

Give your answer to 1 decimal place.

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